What Is Fuzzy Logic?

Foundations of Fuzzy Logic
Logical Operations
Now that you understand the fuzzy inference, you need to see how fuzzy
inference connects with logical operations.
The most important thing to realize about fuzzy logical reasoning is the fact
that it is a superset of standard Boolean logic. In other words, if you keep the
fuzzy values at their extremes of 1 (completely true), and 0 (completely false),
standard logical operations will hold. As an example, consider the following
standard truth tables.
A B A and B A B A or B A not A
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
AND
OR
NOT
Now, because in fuzzy logic the truth of any statement is a matter of degree,
can these truth tables be altered? The input values can be real numbers
between 0 and 1. What function preserves the results of the AND truth table
(for example) and also extend to all real numbers between 0 and 1?
One answer is the min operation. That is, resolve the statement A AND B,
where A and B are limited to the range (0,1), by using the function min(A,B).
Using the same reasoning, you can replace the OR operation with the max
function, so that A OR B becomes equivalent to max(A,B). Finally, the
operation NOT A becomes equivalent to the operation 1− A .Noticehowthe
previous truth table is completely unchanged by this substitution.
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